(In this three part series, Walt Kester provides a compendium of tips and hints that will help embedded systems developers speed the design of the printed circuit boards upon which their designs are based.)

Printed circuit boards (PCBs) are by far the most common method of assembling modern electronic circuits. Composed of a sandwich of insulating layer (or layers) and one or more copper conductor patterns, they can introduce various forms of errors into a circuit, particularly if the circuit is operating at either high precision or high speed. PCBs, then, act as “unseen” components wherever they are used in precision circuit designs.

Since embedded designers don’t always consider the PCB electrical characteristics as additional components of their circuit, overall performance can easily end up worse than predicted. This general topic, manifested in many forms, is the focus of this series of articles.

PCB effects that are harmful to precision circuit performance include leakage resistances; spurious voltage drops in trace foils, vias, and ground planes; the inﬂuence of stray capaci­tance, dielectric absorption (DA), and the related “hook.” In addition, the tendency of PCBs to absorb atmospheric moisture, hygroscopicity, means that changes in humidity often cause the contributions of some parasitic effects to vary from day to day.

In general, PCB effects can be divided into two broad categories: those that most noticeably affect the static or dc operation of the circuit and those that most noticeably affect dynamic or AC circuit operation.

Another very broad area of PCB design is the topic of grounding. Grounding is a problem area in itself for all analog designs, and it can be said that implementing a PCB-based circuit doesn’t change that fact. Fortunately, certain principles of quality grounding, namely the use of ground planes, are intrinsic to the PCB environment. This factor is one of the more signiﬁ­cant advantages to PCB-based analog designs, and an appreciable amount of this appendix is focused on this issue.

Some other aspects of grounding that must be managed include the control of spurious ground and signal return voltages that can degrade performance. These voltages can be due to external signal coupling, common currents, or simply excessive IR drops in ground conductors. Proper conductor routing and sizing as well as differential signal handling and ground isolation tech­niques enable control of such parasitic voltages.

One ﬁnal area of grounding to be discussed is grounding appropriate for a mixed-signal, ana-log/digital environment. This topic is the subject of many application calls, and it is certainly true that interfacing with ADCs (or DACs) is a major part of the system design, and thus it shouldn’t be overlooked. Indeed, the single issue of quality grounding can drive the entire lay­out philosophy of a high-performance mixed-signal PCB design—as well it should.

Resistance of Conductors

Every engineer is familiar with resistors, although perhaps fewer are aware of their idiosyn­crasies. But too few engineers consider that all the wires and PCB traces with which their systems and circuits are assembled are also resistors. In higher-precision systems, even these trace resistances and simple wire interconnections can have degrading effects. Copper is not a superconductor—and too many engineers appear to think it is! Figure C.1 belowillustrates a method of calculating the sheet resistance R of a copper square, given the length Z, the width X, and the thickness Y.

At 25ºC the resistivity of pure copper is 1.72410–6 Ωcm. The thickness of standard 1-ounce PCB copper foil is 0.036 mm (0.0014). Using the relations shown, the resistance of such a standard copper element is therefore 0.48 Ω/square.

One can readily calculate the resistance of a linear trace by effectively “stacking” a series of such squares end to end, to make up the line’s length. The line length is Z and the width is X, so the line resistance R is simply a prod­uct of Z/X and the resistance of a single square, as noted in the ﬁgure.

For a given copper weight and trace width, a resistance/length calculation can be made. For example, the 0.25 mm (10 mil) wide traces frequently used in PCB designs equates to a resist-ance/length of about 19 mΩ/cm (48 mΩ/inch), which is quite large. Moreover, the temperature coefﬁcient of resistance for copper is about 0.4%/ºC around room temperature. This is a factor that shouldn’t be ignored, in particular within low-impedance precision circuits, where the TC can shift the net impedance over temperature.

As shown in Figure C.2 below, PCB trace resistance can be a serious error when conditions aren’t favorable. Consider a 16-bit ADC with a 5 kΩ input resistance, driven through 5 cm of 0.25 mm wide 1 oz PCB track between it and its signal source. The track resistance of nearly 0.1 Ω forms a divider with the 5 kΩ load, creating an error. The resulting voltage drop is a gain error of 0.1/5000 (�0.0019%), well over 1 LSB (0.0015% for 16 bits).

So, when dealing with precision circuits, the point is made that even simple design items such as PCB trace resistance cannot be dealt with casually. There are various solutions to address this issue, such as wider traces (which may take up excessive space), the use of heavier copper (which may be too expensive), or simply choosing a high-impedance converter. But the most important thing is to think it all through, avoiding any tendency to overlook items that appear innocuous on the surface.

Figure C.2: Ohm’s Law predicts _1 LSB of error due to drop in PCB conductor.

Voltage Drop in Signal Leads: Kelvin” Feedback

The gain error resulting from resistive voltage drop in PCB signal leads is important only with high precision and/or at high resolutions (the Figure C.2 example) or where large signal currents ﬂow. Where load impedance is constant and resistive, adjusting overall system gain can compensate for the error. In other circumstances, it may often be removed by the use of “Kelvin” or “voltage sensing” feedback, as shown in Figure C.3 below.

Figure C.3: Use of a sense connection moves accuracy to the load point.

In this modiﬁcation to the case of Figure C.2, a long resistive PCB trace is still used to drive the input of a high-resolution ADC, with low input impedance. In this case, however, the volt­age drop in the signal lead does not give rise to an error, because feedback is taken directly from the input pin of the ADC and returned to the driving source. This scheme allows full accuracy to be achieved in the signal presented to the ADC, despite any voltage drop across the signal trace.

The use of separate force (F) and sense (S) connections at the load removes any errors result­ing from voltage drops in the force lead, but of course may only be used in systems where there is negative feedback. It is also impossible to use such an arrangement to drive two or more loads with equal accuracy, since feedback may only be taken from one point. Also, in this much-simpliﬁed system, errors in the common lead source/load path are ignored, the assumption being that ground path voltages are negligible. In many systems this may not nec­essarily be the case, and additional steps may be needed, as will be detailed later in this series.